Polyhedron.to_linear_program should return the MIP variable used

[mkoeppe]

#18815 introduced Polyhedron.to_linear_program -- but there's very little one can do with it.
To

• set an objective other than the default 0;
• access an optimal solution vector after solving,
  one needs the MIP variable (x in the code of to_linear_program). Currently the only way to do anything is by using the MIP backend.

I would propose to return x as a second return value, but this of course changes the interface.

CC: @nathanncohen @vbraun @videlec @fchapoton @dimpase @jdemeyer

Component: geometry

Author: Matthias Koeppe

Branch/Commit: 280ba21

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/20301

[dimpase]

comment:1

well, you may have a parameter governing what you return, and defaulting to not returning x, then the interface
is not changed, it is extended (i.e. no need to deprecate anything etc etc).

   def to_linear_program(self, solver=None, return_variable=False):
       ...

[mkoeppe]

Branch: u/mkoeppe/polyhedron_to_linear_program_should_return_the_mip_variable_used

[mkoeppe]

comment:3

OK, I've followed your suggestion.
Needs review.

---

New commits:

280ba21

Polyhedron.to_linear_program: Optional argument return_variable

[mkoeppe]

Commit: 280ba21

[mkoeppe]

Author: Matthias Koeppe

[dimpase]

comment:6

looks good to me.

[vbraun]

comment:7

Reviewer name is missing

[dimpase]

Reviewer: Dima Pasechnik

[vbraun]

Changed branch from u/mkoeppe/polyhedron_to_linear_program_should_return_the_mip_variable_used to 280ba21